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the former meaning a variable finite magnitude increasing
beyond all finite limits (like x in I/a above), while the latter is a
fixed, constant magnitude lying beyond all finite magnitudes, it
happens only too often that they are confused.'
Cantor goes on to state that misuse of the infinite in mathe-
matics had justly inspired a horror of the infinite among careful
mathematicians of his day, precisely as it did in Gauss. Never-
theless he maintains that the resulting 'uncritical rejection of
the legitimate actual infinite is no less a violation of the nature
of things [whatever that may be - it does not appear to have
been revealed to mankind as a whole], which must be taken as
they are' - however that may be. Cantor thus definitely aligns
himself with the great theologians of the Middle Ages, of whom
he was a deep student and an ardent admirer.
Absolute certainties and complete solutions of age-old pro-
blems always go down better if well salted before swallowing.
Here is what Bertrand Russell had to say in 1901 about
Cantor's Promethean attack on the infinite.
'Zeno was concerned with three problems. ... These are the
problem of the Infinitesimal, the infinite, and continuity., ..
From his day to our own, the finest intellects of each generation
in turn attacked these problems, but achieved, broadly speak-
ing, nothing.. , . Weierstrass, Dedekind, and Cantor ... have
completely solved them. Their solutions ... are so clear as to
leave no longer the slightest doubt of difficulty. This achieve-
ment is probably the greatest of which the age can boast. ...
The problem of the infinitesimal was solved by Weierstrass, the
solution of the other two was begun by Dedekind and definitely
accomplished by Cantor.'*
The enthusiasm of this passage -warms us even to-day,
although we know that Russell in the second edition (1924) of
his and A. N. Whitehead's Prindpia Mathematica admitted
that all was not well with the Dedekind 'cut' (see Chapter 27),
which is the spinal cord of analysis. Nor is it well to-day. More
is done for or against a particular creed in science or mathe-
* Quoted from R. E. Moritz' Memorabilia Mathcmatica, 1914. The
original source is not accessible to me.